The goal of exploration seismology is to find oil and gas reservoirs
by seismically imaging the earth's reflectivity distribution.
Towards this goal, exploration geophysicists
perform seismic experiments ideally equivalent to that shown
in Figure 1.
Here,
the source excites seismic waves, and the resulting
primary reflections are recorded by a geophone located
at the source position. If we assume
only primary reflections then this
defines
the ideal zero-offset (ZO) experiment.
For now
we assume
a magic filter (to be described later as data processing)
that eliminates all events but primary reflections.

A seismic source is usually some mechanical device or explosive that thumps the earth,
and a geophone records the time history
of the earth's vertical particle velocity,
denoted as a seismic
trace
d(x,z=0,t).
Larger amplitudes on the Figure 1 traces
correspond to faster ground motion and the up-going (down-going) motion
is denoted here by the blackened (unblackened) lobes.
The strength of these amplitudes is roughly proportional
to the reflectivity strength m(x,z) of the corresponding
reflector.
Assuming a constant density and
a 1-D medium , the reflectivity m(x,z)
is roughly defined as
as

m(x,z)

(1.1)

where v(z) is the propagation velocity
at depth z.

After recording at one location,
the source and receiver are moved a bit over and the idealized ZO
seismic experiment
is iteratively repeated for different ground positions.
All recorded traces are lined up next to one another and the
resulting section is
defined as a ZO or poststack seismic section, as
shown on the RHS of Figures 1 and 2.
Note that
the depth d of the first reflector
can be calculated by multiplying the 2-way reflection time t by
half the
velocity v of the
first layer, i.e. d = tv/2.

The reflection section in Figure 1 roughly resembles
the actual geology, where one
side of the signal is colored black to help enhance visual
detection of the interface.
Unfortunately,
this experiment and the ZO seismic
section are
ideal because they assume no
coherent noises such as
multiples, out-of-the-plane scattering,
surface waves, converted waves and so on.
In practice, a real ZO experiment cannot generate the ideal seismic section
because the source
also generates strong coherent noise and
near-source scattering energy. To solve this problem,
explorationists
perform non-zero offset experiments (where one shot
shots into many far-offset geophones), filter coherent noise from these data
and make time-shift corrections to the
traces so that they are
roughly equivalent to the ideal ZO traces. The steps for processing these data are described in a later
section.

Figure 1.1:
Figure 1. Earth model on left and
idealized zero-offset (ZO) seismic section on right,
where each trace was recorded by an experiment
where the source has zero offset from the geophone.
The above ZO seismic section represented
by d(x,z=0,t) roughly resembles the earth's reflectivity
model m(x,z) because we unrealistically assume it contains only the primary
reflections.